The present invention relates generally to function graphing and, more specifically, to automatic determination of optimum graph characteristics.
Mathematical functions can be classified as either algebraic or transcendental (nonalgebraic). Algebraic functions are expressions that involve only the algebraic operations of addition, subtraction, multiplication, division, raising to an integer power, and extracting an odd number root or even number root. In terms of graphing, a key difference that distinguishes algebraic functions from transcendental functions is that algebraic functions have a finite number of points of mathematical interest such as: intercepts, extrema, points of inflection, holes, vertical asymptotes, horizontal asymptotes, slant asymptotes, points of discontinuity, isolated points, vertical tangents, vertical cusps, and corners. Transcendental functions, on the other hand, which include the trigonometric functions, can have an infinite number of points of mathematical interest. This means that graphs of algebraic functions are capable of being displayed in a complete graph—one that includes all their points of mathematical interest.
Software packages and many graphing calculators use algorithms that could display complete graphs of functions if the selection of function-specific graphing settings such as x-dimension values and y-dimension values were appropriate. Further, if all the important mathematical features, together with standard auxiliary graphics for illuminating singularities (holes, discontinuities, isolated points, and the various kinds of asymptotes), could be provided for in the function-specific settings, significant features could be more clearly apparent.
What is needed is a system and method to provide an electronic graph of a function in which important mathematical features of the function, including singularities, are clearly apparent, for example, but not limited to, within an optimum viewing window, for example, but not limited to, on a graphing calculator, a personal computer display, a handheld computer, or other type of electronic display. Further, a system and method are needed to provide an efficient way for a user to view mathematical features of a pre-selected function.